Standard Errors & Design Effects

This section contains information on standard errors and design effects for the NLSY79 sample, briefly discussing how to use these two statistical factors. It then includes tables for the first round and for 1996 through 2020. Users interested in the intervening years should review the NLSY79 Technical Sampling Report and Technical Sampling Report Addendum.

Standard errors have been explicitly computed for a number of statistics based upon the entire NLSY79 sample (total, civilian, and military) and a number of sex or race subclasses. Standard errors for other statistics (defined over the entire sample or the subclasses) may be approximated with use of the DEFT factors given in the linked tables. Users who examine the tables will note that CHRR has calculated standard errors for different variables over time. The R program that computed the Standard Errors and Design Effects for survey year 2020 can be accessed in the document NLSY79 Design Effects R Program.docx.

Approximate Standard Errors: Percentages

The following formula approximates a standard error of a percentage:

where:

For example, for 1996 the appropriate DEFT factor for estimating a standard error of the percentage of Hispanic or Latino males who were high school dropouts is 1.17744 (see proportion column, row seven of Table: Deft Factors for Round 17, 1996). Assuming the calculated sample (P) equals 22.19 percent and the unweighted sample estimate size is 946, then:

To approximate the standard error of the corresponding projected population total (NP/100), calculate:

where:

For example, if the projected total population base for Hispanic or Latino males is 1,030,861, the projected number of civilian Hispanic or Latino male high school dropouts is equal to NP/100 or 1,030,861 * 22.19/100 = 228,748. Thus, the approximate standard error for the total number of Hispanic or Latino male high school dropouts is:

Note that the 1.5907 came from the previous calculation.

Approximate Standard Errors: Means

One can compute approximate standard errors for means as follows:

where:

For example, for 1979 the DEFT factor for all Hispanics or Latinos is 1.45699 (see means column, row four of Table 1). To approximate the standard error of the mean number of years of education completed by this subclass, where the weighted element variance is .72955 and the sample size is 77, compute:

Design Effects

Because the samples are multi-stage, stratified random samples instead of simple random samples, respondents tend to come in geographic clusters and clusters of persons tend to be alike in a variety of ways for a variety of reasons. (For more information on the sampling and screening process, users are referred to section on Sample Design & Screening Process in this guide.) For example, there may be cultural differences by locality or ecological differences in labor market conditions. Depending upon the degree of this homogeneity, the conventionally computed standard deviations for the variables, which assume a simple random sample, may be too small. However, by controlling the rate at which particular strata are sampled, multi-stage, stratified random samples can improve upon simple random samples. The ratio of the correct standard error to the standard error computed under the assumption of a simple random sample is known as the design effect. The technical sampling report for the NLSY79 (Frankel, Williams, and Spencer 1983) and its addendum (CHRR) provide design effects for the various strata.  

A single design effect that can be broadly applied to regression analysis cannot be constructed. To illustrate the approximate size of design effects in regression analysis, a regression of rate of pay for the CPS job in 1979 was estimated using race, sex, marital status, and education as explanatory variables. Assuming each of the roughly 200 PSUs has the same number of respondents in the sample of 5,724 persons with observed wages, the design effect was calculated to be 1.52; that is, the true standard errors were larger than the naively computed standard errors by a factor of 1.52. When this exercise was repeated for rate of pay on the CPS job in 1986, the design effect had fallen to 1.37.

This reduction reflects the fact that mobility tends to mix the respondents more uniformly through the country, reducing the clustering of the sample. Many of the persons who started out in the same PSU will have moved to different areas and, hence, no longer share unobservable labor market conditions. These shared unobservable labor market conditions are likely responsible for the spatial correlation of the error terms which generate design effects. Thus, another advantage of longitudinal data is the lessening of design effects over time.

By examining the Geocode data for the NLSY79, it is possible to control for some of the environmental factors generating design effects or, if desired, to compute design effects based upon county or metropolitan area clusters which continue to be present. To facilitate study of design effects, scrambled PSU codes from the 1979 survey are available to persons with authorized access to the NLSY79 Geocode data.

The Technical Sampling Report and Technical Sampling Report Addendum also provide information on design effects.

Table: Deft Factors for Round 1, 1979

Table: Deft Factors for Round 17, 1996

Table: Deft Factors for Round 18, 1998

Table: Deft Factors for Round 19, 2000